SOLUTION: Question: Find the domain of f(x)=log subscript2(6-x). (1)(2,6) (2)(-infinite, 6) (3) (6,infinite) (4) (-6, infinite) which one? thanks for your help.

Question 202608: Question: Find the domain of f(x)=log subscript2(6-x). (1)(2,6) (2)(-infinite, 6) (3) (6,infinite) (4) (-6, infinite) which one? thanks for your help.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

The domain of a function, if not explicitly stated, is all Real numbers except those that would result in something you cannot allow to occur:

zeros in denominators
negative numbers in the radicands of even-numbered roots
Zero or negative arguments to log functions
Other "no-no's" like , etc.

The only thing you need to avoid for f(x) is a zero or negative argument to the log function. Worded positively, we only want to allow x-values that make the argument to the log positive. In other words:
(6-x) > 0
The simplest way to solve this is to add x to both sides:
6 > x
This is our domain. The tricky part is to read this correctly. This says "x is less than 6". (Always read inequalities from where the variable is. Since this inequality has the variable on the right we start reading from the right and read right-to-left! Read this way it says "x is less than 6".)
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